Volumetric Strain Rate Research Articles

Research on the Mechanical Behavior of Styropor Concrete at High Strain Rates

Mechanical behavior of Styropor concrete(EPSC) added with various volumetric fractions of EPS subjected to high strain rates were studied by using the Large-Diameter-SHPB. The infection of volumetric fractions and average strain rate to dynamic properties of EPSC were investigated. The experimental results show that under high strain rate condition, the dynamic strength, dynamic strength increase factor(DIF) and limit strain of EPSC are strain rate dependent, the strain rate effect can be expressed by linear approximations, and the relationship between elastic modulus and average strain rate is independent.With the addition of volumetric fractions of EPS, the impact compressive strength and elastic modulus of EPSC declines, and the toughness of EPSC is reinforced.

Formulation and validation of a constitutive model for sands in monotonic shear

A constitutive model for sands in monotonic shear is presented. The model is designed to simulate the behavior of sands in the whole stress and strain range of engineering interest with enough accuracy for practical usage. Material parameters were chosen to be state independent and easy to calibrate using conventional testing procedures. The formulation is based on effective stresses, pressure-dependent hyperelasticity, non-associative elastoplasticity, an isotropic hardening law and Rowe’s stress-dilatancy theory. The implementation of Rowe’s stress-dilatancy theory within the framework of elastoplasticity theory is discussed. It is found that Rowe’s theory produces a volumetric plastic strain rate function that has a discontinuity in its first derivative w.r.t. stress, and a smoothed form is proposed instead. Finally, some experimental tests are simulated and the results are briefly discussed.

Research on rigid/visco-plastic element-free Galerkin method and key simulation techniques for three-dimensional bulk metal forming processes

The element-free Galerkin method is introduced into the analysis of three-dimensional bulk metal forming processes according to flow formulation for rigid/visco-plastic material. The transformation method is used to impose the essential boundary condition directly. The stiffness matrix equation is derived according to incomplete generalized variational principle. And the corresponding key simulation techniques are developed. The case that matrix A(x) appears irreversible is discussed, and the approaches for treating with this problem are given. Volumetric strain rate method is proposed for releasing the volume locking problem. The method for describing shapes of dies is presented. In order to impose arbitrarily shaped boundary conditions in three-dimensional problems, the local coordinate system is established and the transformation matrix between the local coordinate system and the global coordinate system is calculated. Methods for exerting velocity and frictional contact conditions are introduced. Dynamic adjustment techniques for the boundary of the workpiece including the contact/detachment judgment criterion and the method for modifying the contact nodes’ positions are given. Finally, the effectiveness of the method and key techniques is demonstrated by simulating a two-stage three-dimensional forging process.

P1‐nonconforming quadrilateral finite element for topology optimization

AbstractThis investigation focuses on an alternative approach to topology optimization problems involving incompressible materials using the P1‐nonconforming finite element. Instead of using the mixed displacement‐pressure formulation, a pure displacement‐based approach can be employed for finite element formulation owing to the Poisson locking‐free property of the P1‐nonconforming element. Moreover, because the P1‐nonconforming element has linear shape functions that are defined at element vertices, it has considerably fewer degrees of freedom than other quadrilateral nonconforming elements and its implementation is as simple as that of the conforming bilinear element. Various problems dealing with incompressible materials and pressure‐loaded structures found in published works are solved to verify the applicability of the proposed method. The application of the method is extended to the optimal design of fluid channels in the Stokes flow. This is done by expressing pressure in terms of volumetric strain rates and developing a velocity‐field‐only finite element formulation. The optimization results obtained from all the problems considered in this study are in close agreement with those found in the literature. Copyright © 2010 John Wiley & Sons, Ltd.

Stress state dependence of in-reactor creep and swelling: Part I: Continuum plasticity model

Irradiation induced swelling of reactor core materials may jeopardize safe and reliable operation of fast reactors due to swelling-induced distortion and interference of core components. The principles of incremental continuum plasticity are used here to develop constitutive equations that can be used to conduct engineering evaluations of these potential problems. The equations are used in Part II to analyze previously unreported in-reactor creep and swelling data obtained ca. 1977–1979 as part of the US breeder reactor program. Results of this stress state experiment showed for the first time that a deviatoric stress can affect volumetric swelling. The constitutive equations developed here predict that, in the presence of significant swelling, deviatoric and volumetric strain rate components each are functions of both deviatoric and hydrostatic components of stress for both linear and non-linear creep.

A destructuration theory and its application to SANICLAY model

Many natural clays have an undisturbed shear strength in excess of the remoulded strength. Destructuration modeling provides a means to account for such sensitivity in a constitutive model. This paper extends the SANICLAY model to include destructuration. Two distinct types of destructuration are considered: isotropic and frictional. The former is a concept already presented in relation to other models and in essence constitutes a mechanism of isotropic softening of the yield surface with destructuration. The latter refers to the reduction of the critical stress ratio reflecting the effect of destructuration on the friction angle, and is believed to be a novel proposition. Both the types depend on a measure of destructuration rate expressed in terms of combined plastic volumetric and deviatoric strain rates. The SANICLAY model itself is generalized from its previous form by additional dependence of the yield surface on the third isotropic stress invariant. Such a generalization allows to obtain as particular cases simplified model versions of lower complexity including one with a single surface and associative flow rule, by simply setting accordingly parameters of the generalized version. A detailed calibration procedure of the relatively few model constants is presented, and the performance of three versions of the model, in descending order of complexity, is validated by comparison of simulations to various data for oedometric consolidation followed by triaxial undrained compression and extension tests on two structured clays. Copyright © 2009 John Wiley & Sons, Ltd.

Anisotropic creep model for soft soils

In this paper a new anisotropic model for time-dependent behaviour of soft soils is presented. The formulation is based on a previously developed isotropic creep model, assuming rotated Modified Cam Clay ellipses as contours of volumetric creep strain rates. A rotational hardening law is adopted to account for changes in anisotropy due to viscous strains. Although this will introduce some new soil parameters, they do not need calibration as they can be expressed as functions of basic soil parameters through simple analytical expressions. To start with, the one-dimensional response of the model is discussed, making it possible to explore how the model is capable of capturing key features of viscous soft soil behaviour. Subsequently, the three-dimensional generalisation of the model is presented, followed by comparison with experimental data, showing good agreement in both triaxial undrained compression and extension. In the authors' opinion, the simple formulation of the model makes it attractive for use in engineering practice.

Releasing Algorithm for Volumetric Locking in Metal Forming Process Simulation Based on Element-Free Galerkin Method

The meshless methods effectively deal with large material distortion simulation. Based on the rigid (visco)plastic material model, the element-free Galerkin method (EFGM) is introduced to simulate the metal forming processes. Aiming at the volume locking and pressure oscillation during EFGM analysis, a volumetric strain rate mapping method is proposed based on pressure projection method. The releasing algorithm is established by modifying the volumetric strain rate in the functional equation. The volumetric strain rate calculated according to velocity field is mapped onto a lower-order space to reduce the number of independent discrete constrain equations. The numerical example shows that the releasing algorithm can effectively eliminate the volumetric locking and pressure oscillation without the expense of employing large support size in the rigid-plastic meshless method.

A model for an adaptable axisymmetric extrusion die with a bearing length

Abstract The adaptable design method uses upper bound models to determine die shapes that meet specified criteria, such as minimizing distortion in the product. This method has been developed for the axisymmetric extrusion process. In order to extend the methodology to the three-dimensional extrusion of a non-axisymmetric shape, the deformation zone in the upper bound model would need to be extended into the bearing region of the extrusion die. The necessary equations and conditions needed to make such an extension are presented in this paper. Finite element modeling (FEM) is used to compare the results of extrusion through dies designed by the adaptable die design method, for a model with the deformation zone extended into the bearing region, to a model without such an extension. The results indicate that the upper bound model incorporating a bearing length provides a realistic flow field. The results also demonstrate that the upper bound model can be used to analyze a multi-sectioned die, so long as: (1) the die surface and first derivative of the surface are continuous between sections, and (2) calculation of the internal power of deformation is made for each section separately. The results provide further support for the findings that the average effective strain and the volumetric effective strain rate deviation are robust criteria, which can be used to determine optimal adaptable die shapes with an upper bound model.

Pressure calculations in disperse and continuous multiphase flows

In many models for disperse two-phase flows, the pressure of the disperse phase is often assumed to be the same as that of the continuous phase, or differ only by an amount caused by the surface tension. This type of model is referred to as an equilibrium pressure model. Recent research indicates that the stress difference between the phases caused by dynamics of the motion can be significantly important in the modeling of disperse two-phase flows. Although this difference is still ignored in most calculations of disperse multiphase flows for various reasons, when an equilibrium pressure model is applied to continuous multiphase flows, a conceptual difficulty arises. For instance, the equilibrium pressure model cannot be used to study the tensile break of a sponge with interconnected pores, because the air in the pores can never go into tension while the sponge material does not break without tension. To avoid this conceptual difficulty, a multipressure model is introduced for continuous multiphase flows by analyzing and then modifying the implicit assumption about the volumetric strain rates involved in the equilibrium pressure model. Numerical implementations of the multipressure model are discussed. An example using the multipressure model is presented.

RELEASING ALGORITHM FOR VOLUME LOCKING IN RIGID-PLASTIC MESHLESS METHOD

The meshless Galerkin method is introduced to the analysis of the metal forming processes. The fundamental theories and basic equations for the rigid-plastic meshless method are developed. The releasing of the volume locking encountered in the analysis of the metal plastic forming problems is studied and a releasing algorithm is established by modifying the volumetric strain rate in the functional equation. The volumetric strain rate calculated according to velocity field is mapped onto a lower-order space to reduce the number of independent discrete constraint equations. The algorithm can release the volumetric locking without the expense of employing large support size in the rigid-plastic meshless method. A typical metal forming problem is analyzed. The results show that the algorithm can effectively release the volumetric locking problem.

Gouge formation by dynamic pulverization during earthquake rupture

It is proposed here that fault gouge forms by rock pulverization within the tip region of a fast propagating earthquake due to the intensity of stress and rates of strain in this zone. To examine this mechanism, we calculate the deformation conditions of a dynamic shear fracture propagating close to the limiting Rayleigh wave velocity. The mechanical conditions close to the fracture tip are extreme: tensile stresses approach 5 GPa, volumetric strain rates exceed 10 5 s − 1 , and volumetric expansion alternates with volumetric contraction. It is expected that a localized zone a few millimeters wide will be pulverized under these conditions. This mechanism of dynamic gouge formation provides new insight to recent observations of the texture of gouge from the San Andreas fault-zone and from rupture zones in South African mines. Further, as such extreme conditions develop only during fast propagating earthquakes, presence or absence of pulverized gouge may serve as an indicator of earthquake propagation velocity.

Performance evaluation of different model mixers by numerical simulation

Mixing performance of four types of mixers was investigated for Newtonian and shear-thinning fluids using numerical simulation. The four mixers considered were with the following blade designs: rectangular blade, one Z-blade, two Z-blades, and three rotating pins. Finite element method was used to compute velocity profiles, pressure and stress distributions in the mixing chamber. Mixing effectiveness was evaluated by the flow number and volumetric strain rate. It was demonstrated that shear flow was dominant in rectangular, one Z-blade, and two Z-blade mixers; in the mixer with three rotating pins elongational flow was significant making it the most effective for dispersive mixing. The largest volumetric strain rate was predicted in the mixer with two Z-blades. The rectangular blade mixer was deemed due to a large stagnant region observed. The stagnant regions were larger near the wall for all mixers when shear-thinning fluid was used compared to the Newtonian fluid. Thus, for shear-thinning fluids, to achieve the same mixing effect as with Newtonian fluid, either a smaller gap between the blade and the wall or a higher blade speed is required. Overall, the two Z-blade mixer was considered the best in terms of mixing effectiveness.

Laboratory deformation of granular quartz sand: Implications for the burial of clastic rocks

We explore the influence of mechanical deformation in natural sands through experiments on water-saturated samples of quartz sand. Stresses, volumetric strain, and microseismicity (or acoustic emission, AE) rates were monitored throughout each test. Deformation of quartz sand at low stresses is accommodated by granular flow without significant grain breakage, whereas at high stresses, granulation and cataclastic flow are dominant. Sands deformed under isotropic conditions show compactive strains with an inverse power-law dependence of macroscopic crushing strength on mean grain size. Triaxial compression at high effective pressures produces compactive strain and a high AE rate associated with considerable particle-size reduction. Triaxial compression at low effective pressure produces dilatant granular flow accommodated by grain boundary frictional sliding and particle rotation. On the basis of experiment results, we predict the evolution of porosity and macroscopic yield strength as a function of depth for extensional and contractional basins. Sand strength increases linearly with depth for shallow burial, whereas for deep burial, strength decreases nonlinearly with depth. At subyield stresses, porosity evolves as a function of applied mean stress and is independent of distortional stress. Our predictions are in qualitative agreement with observations of microfracture density obtained from laboratory creep-compaction experiments and with natural sandstones of the Gulf of Mexico basin. Mechanical deformation contributes as much as a 30% increase to fluid pressure evolution, which has particular application to sedimentary systems that display zones of fluid overpressure. Furthermore, deformational strains cannot be fully recovered during uplift, erosion, and unloading of a sedimentary basin.

Effects of volumetric ice content and strain rate on shear strength under triaxial conditions for frozen soil samples

AbstractA set of triaxial constant strain rate and constant stress tests was performed on artificially frozen soil samples to study the effect of the volumetric ice fraction, strain rate and also confining stress on the mobilized shear strength. In general, the peak shear strength increased with decreasing volumetric ice content and increasing strain rate. Pure ice samples, however, showed a peak shear strength that was higher than that for those containing about 80% ice by volume for a similar strain rate, although the loss in strength after this maximum was usually much more pronounced, reaching a lower large strain strength than that for frozen sands. The influence of the ice in samples with low ice contents was primarily noticeable at low strains, whereas the large strain behaviour was very similar to that of the unfrozen material. The tests showed the dependency of the mechanical failure and deformation mode of frozen soils on the loading conditions. It could be demonstrated further that large strains have a significant influence on the strength of frozen geo‐materials and therefore efforts should be made to establish in situ strain states when analysing the stability of frozen slopes. Copyright © 2004 John Wiley & Sons, Ltd.

Discrete element modelling of cyclic loading of crushable aggreates

This paper examines the discrete element modelling of cyclic loading of an aggregate of crushable sand grains. Each grain of sand is modelled as an agglomerate of balls bonded together. The aggregate is subjected to compaction followed by isotropic normal (plastic) compression, and then unloaded to half the maximum applied stress. The aggregate is then subjected to cyclic loading to a maximum stress ratio of 0.8. The aim of the paper is to examine the reduction of the rate of axial strain with number of cycles, and to determine the relative influences of volumetric strain and shear strain rates on the axial strain rate. In particular, the paper aims to show whether particle breakage is mainly related to the accumulation of volumetric strain. This is found to be the case, which is consistent with proposals by other authors that plastic hardening under monotonic loading is due to particle fracture.

Shear-enhanced compaction during non-linear viscous creep of porous calcite–quartz aggregates

In this paper, we extend the previous studies of semi-brittle flow of synthetic calcite–quartz aggregates to a range of temperatures and effective pressures where viscous creep occurs. Triaxial deformation experiments were performed on hot-pressed calcite–quartz aggregates containing 10, 20 and 30 wt% quartz at confining pressure of 300 MPa, pore pressures of 50–290 MPa, temperatures of 673–1073 K and strain rates of 3.0×10−5/s, 8.3×10−5/s and 3.0×10−4/s. Starting porosity varied from 5 to 9%. We made axial and volumetric strain measurements during the mechanical tests. Pore volume change was measured by monitoring the volume of pore fluid that flows out of or into the specimen at constant pore pressure. Yield stress increased with decreasing porosity and showed a dependence on effective pressure. Thus, the yield stress versus effective pressure can be described as a yield surface with negative slope that expands with decreasing porosity and increasing strain hardening, gradually approaching the envelope of strength at 10% strain, which has a positive slope. Creep of porous rock can be modeled to first order as an isolated equivalent void in an incompressible nonlinear viscous matrix. An incremental method is used to calculate the stress–strain curve of the porous material under a constant external strain rate. The numerical simulations reproduce general trends of the deformation behavior of the porous rock, such as the yield stress decreasing with increasing effective pressure and significant strain hardening at high effective pressure. The drop of yield stress with increasing porosity is modeled well, and so is the volumetric strain rate, which increases with increasing porosity.

土質材料におけるせん断変形挙動の降伏曲線形状への依存性

The volumetric change accompanying with plastic shear deformation causes the dependency of q on p where p and q respectively represent the hydrostatic pressure and the equivalent deviatoric stress in yielding. Their dependency is called yield curve or yield function. In geomechanics Cam-clay and cap models have been frequently used as yield curve. In the last report we examined the shapes of yield curve based on the deformation behaviour observed in the published experiments where a parallel piped specimen was compressed under plane strain condition or a cylindrical specimen was extended in axial direction increasing confining pressure. In many cases the shape of yield curve were different from those in Cam-clay and cap models. In this paper the inverse prediction is discussed where the deformation behaviour is predicted according to the yield curve and hardening charcteristics obtained in the last report. First, the method of the inverse treatment is proposed, and then the comparison is made between predicted behaviour and the observed one. On the whole the inverse prediction is successful, but an abnormal prediction arises in the case that the term ƒr+α tends to zero or to be negative where ƒr;, represents the ratio of compressive volumetric strain rate to distortional strain rate and a is the hardening ratio constant. So far geomechanics has been developed under the condition of α=0. In such framework the abnormal prediction can be brought about at positive volumetric strain rate, and so introducing of hardening ratio constant must be considered. Stress point (p, q) moves with progressive deformation. Under plane strain compression the stress point approaches to the critical state line with the increase of deformation, and finally reaches to it. It is proved that the movement of stress point always stops on the critical state line regardless of the hardening characteristics of deforming soil.

Yielding Behaviour in Strain Controlled Compactions of Metal Powder Assembles.

Metal powder assembles show some volumetric change under irreversible deformation, and their yield function (yield curve) is represented in the space of equivalent deviatoric stress q and hydrostatic pressure p. In the mechanics of metal powder assembles yield curves are assumed to be contours of constant density. However, there is something questionable in this concept. We already examined the consistency of the concept referring to the experimental data of tri-axial compression tests carried out in the past by other investigators, who compressed cylindrical specimens subjected to constant lateral pressure. The results showed that the concept of constant density was inconsistent with the actual constitutive behaviour under the assumption that associated flow rule is applicable and yield curve expands in a similar shape with increasing of compressive deformation. Here, we newly referred to the data obtained from compaction tests by Brown and A-Chedid who collected them using uni- and tri-axial strain control systems. In these compaction tests the direction of stress vector (p, q) do not change largely, and so whole view of yield curve is not obtainable. But the correspondence between directions of stress and strain rate vectors can be determined in the compactions. The comparison of the results with those in compression tests does not show good agreement. That suggests the necessity of inspection on the suitability of constitutive model used in the mechanics of metal powder assembles. Hardening strain rate ey is defined here which is composed of volumetric strain rate ep and equivalent deviatoric one eq accompanying with constant parameter. Finally, it is found that this definition is valid from the view point of inherent characteristic of hardening.

The change in effective stress associated with shrinkage from gas desorption in coal

Volumetric shrinkage associated with gas desorption from the coal matrix has a significant influence on the stress field. This is of particular practical importance around headings in underground coal mining, as it controls the permeability to gases and will affect the strength of the strata. In this paper, the volumetric changes of the coal matrix were monitored for four different gases (methane, nitrogen, carbon dioxide and helium) on a sample from the South Island, New Zealand. The specimen was initially saturated with the gas to a pressure of 4 MPa. The volumetric strains were recorded during the adsorption and desorption processes. The overall shrinkage coefficient, C m, of coal matrix was found to be 1.2×10 −3 MPa −1 for methane and 5.2×10 −3 MPa −1 for carbon dioxide desorption. A series of loading/unloading cycles applied by gas pressure were performed on the specimen using a non-adsorbable gas (helium). The results showed elastic behaviour of the sample with some effective stress recovery associated with the incremental change in pressure. The elastic properties were determined from a uniaxial test on the sample. From this data and using Terzaghi's equation, a relationship was established between the effective stress and gas pressure. It was also found that the slope of volumetric strain rate and gas pressure is a function of coal permeability, which could be used to estimate permeability.